Before displaying the numerical results, we need to introduce how to fix the values of these involved parameters, which include the masses and the related coupling constants. For the mass and width of the \(\Upsilon (10753)\) , the measured central values from the Belle Collaboration, \(m_{\Upsilon (10753)}=10.753\)  GeV and \(\Gamma _{\Upsilon (10753)}=35.5\)  MeV [1]}, are adopted in our calculation. For the mass of the \(\Upsilon (1^3D_2)\) , we take its experimental result \(m_{\Upsilon (1^3D_2)}=10.164\)  GeV [2]}. For the masses of the \(\Upsilon (1^3D_1)\)  and \(\Upsilon (1^3D_3)\)  still missing in experiment, the theoretical results \(10.153\)  and \(10.170\)  GeV predicted in Ref. [3]} are taken in our calculation, respectively. Moreover, the PDG values [4]} are used for other involved bottom mesons and \(\eta \)  meson in this work.
